For pie dough: Place flour, baking powder and salt in a mixing bowl and whisk together. Add butter and cut into the dry ingredients using your fingers or a pastry knife until a fine mealy texture forms. Add water, one tablespoon at a time, mixing, until the dough just comes together. Form dough into a flat disc and wrap in plastic wrap. Chill for at least 30 minutes before using.
For filling: Place ham and onions into a small mixing bowl and toss together. Add eggs and milk and mix together. Fold in cheeses until fully incorporated. (you should have more of a loose paste texture, instead of a runny filling). Season with salt and pepper and set aside until ready to use.
To assemble: Preheat oven to 425°F. Roll chilled dough out onto a clean, lightly floured surface. Roll until slightly thinner than 1/8 inch thick . Cut out 4 inch circles, using a circle cutter, and fill the center of each circle with 1-2 tablespoons of filling. Continue until all of the dough and filling have been used. (For egg wash: In a small mixing bowl beat together 1 egg and 2 tablespoon water.) Brush egg wash around the edge of each circle and fold together. Egg wash the sealed seam and starting from one edge push the seam over and squeeze the dough slightly. Use the dough you have squeezed and fold it over the seam again. Continue squeezing and folding until you have crimped the entire seam of the quiche pocket. Place pockets onto a baking sheet, lined with parchment, and pierce the top of each to allow steam to escape, while baking. Place pockets in the refrigerator for about 30 minutes. Brush the tops with remaining egg wash and bake for 25 to 30 minutes or until golden brown and the filling has set. Allow to cool for 5 minutes before serving.
For mornay sauce: Melt butter in a small saucepan over medium heat. Sprinkle flour over surface and whisk together for 2 to 3 minutes. Add the milk and whisk together until no lumps remain and the mixture is thick enough to coast the back of a spoon. Toss cheeses in lemon juice and whisk into the béchamel sauce. Continue to whisk until no lumps remain. Season with salt and pepper and stir. Serve as a dipping sauce for quiche pockets.